The independent paymaster overseeing BP oil spill claims admits that he oversold the speed and transparency of the program he took over a month ago, but his office still promises to make businesses whole.

Critics have charged payments have been slow in coming, and often for just pennies on the dollar, and that people have had difficulty getting information on their claims.

But Kenneth Feinberg, administrator of the Gulf Coast Claims Facility, told NBC News Thursday that his office is quickly catching up on payments to people who show they lost money due to the April oil spill.

In the first month of its program, the Gulf Coast Claims Facility says it’s paid 26,572 claims more than $349,271,301.

"We are being much more generous than BP," Feinberg said. "This will be a very generous program."

"We're working 24 hours a day, seven days a week in three shifts," he said. "We're doing now about 1,500 claims a day. I think that we're rapidly gaining the high ground now."

More than 200 million gallons of oil spewed from BP's undersea well after the Deepwater Horizon exploded off the Louisiana coast on the night of April 20, killing 11 workers. Besides spoiling fragile coastal ecology, the spill sank much of the area economy. Fisherman could not catch and sell tons of seafood, and thousands of tourists canceled plans to visit areas where oil and tar balls marred once pristine beaches from Louisiana to Florida.

"We haven't processed all of the claims as quickly as we should have," Feinberg told NBC News. "I oversold this program at the beginning, and I'm paying the price for it."

At recent town hall meetings along the Gulf, Feinberg has been hit with anger and frustration.

At a meeting last week in the Gulf Coast town of Orange Beach, Ala., the mayor took a poll. Of an estimated 1,000 attending, he asked those who'd been made whole to stand. No one did. Only 16 had received checks.

Jeff Hardy owns a shoe and apparel business and says his losses are now more than $1 million. He says he received one check for $5,000 under BP, and nothing from Feinberg. At the town meeting, he told Feinberg, “I’m to the point now where I don’t know if my doors will be open in another month.”

Sheila Newman and Sheryl Lindsay, twins who own and operate Orange Beach Weddings, a destination wedding service that plans weddings on the beach, did receive an additional emergency payment of $7,700 last week, in addition to an earlier payment of $21,000. But that's a small percentage of the total business they say the spill cost them in lost weddings during the spring and summer: a total of $240,000. They say they may have to file for bankruptcy next week.

"We feel like we deserve what we lost," Newman says. "And that's all we're asking for — is give us what we lost.”

As for claims unpaid or underpaid, Feinberg blamed lack of documentation on the part of people seeking money. "I would say to those businesses that have been receiving less than what they asked for, they just don't have the backup to justify it," he said.

But Hardy says he’s provided 1,700 pages to back up his claim. “Now I’m being told since I’ve got so much information on the table that it cannot be processed.”

At the meeting, Feinberg responded, "That’s ridiculous.”

Feinberg said time will show that the program is fair, and though he is being paid a flat fee by BP to administer the program, he said he is no tool of the oil industry.

"You hear about the angry claimant, or the frustrated claimant," Feinberg said. "I hear from them every day, more than you do. I also hear from many people: 'Thank you, Mr. Feinberg. You saved my home, you saved my business.' "

Feinberg is a Washington lawyer who previously oversaw the federal Sept. 11 Victim Compensation Fund, which distributed nearly $7 billion to more than 5,000 victims and families of victims of the terrorist attack. He also managed the Hokie Spirit Memorial Fund, set up for victims' families following the 2007 Virginia Tech mass shooting.

Feinberg said that as with Sept. 11, the beginning of a compensation program is difficult.

"It's only act one here. ... Sometimes it takes a while to turn people around, and their thinking around," he said.

Asked if his bottom line is making people whole, Feinberg said, "Absolutely. If I don't do that, I've failed."